A276556 a(n) = smallest prime p such that (smallest prime > p^2) == p^2 + 4n^2, n>=1.

5, 281, 461, 4937, 25367, 75997, 1193909, 3464389, 48591863, 23674667, 22486333, 1648510979, 12708853771, 25139472583, 53498475287

Offset: 1

Author

Zak Seidov, Apr 18 2017

Keywords

• nonn
• more

Examples

			5^2+4*1^2=29, 281^2+4*2^2=78977, 461^2 + 4*3^2=212557 (all prime).
		

Crossrefs

Cf. A007491, A053000.

Programs

Mathematica

Table[p = 2; While[NextPrime[p^2] != p^2 + 4 n^2, p = NextPrime@ p]; p, {n, 8}] (* Michael De Vlieger, Apr 22 2017 *)

PARI

a(n) = {forprime(p=2, , if (nextprime(p^2+1) == p^2 + 4*n^2, return (p)););} \\ Michel Marcus, Apr 19 2017

Extensions

a(13)-a(15) from Rémy Sigrist, Apr 28 2017